The End Plus One

There is never an end. For when you think you reached the end, you can always add one.

For example, when I was about three, I learned about the numbers and how to count by thumbing through the encyclopedia and looking at the page numbers. For a while I thought there were no numbers bigger than the 200's. So I thumbed through, looking for what comes after the 200's. I went to 299, and then flipped the page. What did I see? 300. To me this was an enlightening event. For even as we seek to go beyond 2 by adding 1 to get 3, so we go beyond 299 by adding one to get 300.

As I grew older, I learned bigger numbers. A million is 1,000,000. So add one and you get a larger number, namely 1,000,001. Add one to a billion to get 1,000,000,001, a billion and one. A googol is 1 followed by a hundred zeroes. Is that the largest number? No, it is not as big as a googol plus one. A googolplex is one followed by a googol of zeroes. Then one can take one followed by that number of zeroes, and then one followed by that number of zeroes, a googol times. Is that the largest number? No, just add one. That number I just mentioned just happens to be smaller than that number I just mentioned plus one.

Notice that I used some complicated mathematical terminology - taking 10 to high powers. But sometimes you can't get anywhere with that. If you take 1 to the 1 power you get 1. If you take 1 to the hundredth power (one multiplied by itself a hundred times) you still get 1. One to the googol power is 1 and one to the googol superpower (defined as one to the one ... to the one power a googol times) is still 1. Why go to all this when to get past one you need only add one. 1 + 1 = 2. There! We are beyond 1. Now if you take 2 to the googol power you get a number that can't be printed even if the entire universe was used as digits.

Back in the old days people thought the earth was flat. They wondered what would happen if you step off the edge, after you have sailed your ship a million cubits. Well, the answer is simple. You would be out of this world. But you would be able to step off the end. You can sail your ship to a million plus one cubits. You would find out what's beyond a million, and what's beyond the world. But there is a beyond the world, because you can always add one.

Mathematicians have even been able to step off to infinity and beyond. They do this by thinking about all finite numbers. If you think about nothing, which sometimes is hard to do unless you practice Zen meditation, you have thought about something! Namely nothing. There is one and only one nothing, namely 0, and you have thought of it, and you have just reached 1. If you think of both 0 and 1, you have gone beyond 1 to plurality: 2. If you think about the numbers from 0 to 4, you have gone beyond 4. You are thinking of 5 numbers. If you think of the numbers from 0 to 1999, you have gone beyond 1999 into the next millennium, to 2000. That is why I say that 2000 begins the millennium, not 2001. In the same way if you think of all finite numbers, you have gone beyond all finite numbers. You have reached infinity! Mathematicians usually call this number ω, although they sometimes call it aleph-null.

But that's not the end. Just add one! You reach ω + 1, which is one beyond ω and beyond infinity. And you can continue to add one until you have added 1 an infinite number of times. You are now thinking about ω + ω or ω2, omega times 2. And you can continue to add like this, reaching ω3, ωω or ω2, ω3, ωω, ωωω, ... After all this is a number ε0. Now raising ω to the ε0 power should get you to an even bigger infinite, shouldn't it. No, you wind up back at ε0 again. You have gone nowhere. So what do you do? Simple. Just add one. ε0 + 1. Now you can continue with ωε0 + 1 and so forth. There are many other places in the infinite, or transfinite numbers where you can't get anywhere with highfalutin operations, and when you get to that point, you need to add one to keep on going. When you feel like you can't go any farther, just add one.

This applies to ultimate concepts in religion as well. There cannot be a God, as usually defined. This is because you can always add one; you can always go beyond God. Think of the God of Genesis in the Old Testament. He created the heavens and the earth. But he can't be the Ultimate Supreme Being, for who created Him? Once you think you have reached God, you suddenly find God plus one: the Creator of God, and the Supreme Creator of All Gods in All Universes. But that is not the end either. There never is an end. Just add one. Who created this Supreme Creator? Yet another Creator, and so forth. For this reason, it does not make sense to talk about a God. Lao-Tze found this out for he writes about his version of God, The Way, or the Tao: "The Way that you conceive of is not the True Way."

So just add one. If you get stalled in doing something, just add one. One by one, bit by bit the task gets done. If you are burned out, if you get writer's block, if you can't go any farther with what you are doing, if you are at the ε0 of your endeavors, just add one and you will get out of your jam and proceed. In fact, if you just thought you have reached the End of the Internet, you have just added one, for this page is the End of the Internet Plus One.

Jim Blowers
"Just add one."

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